Answer:
A) AAS; B) LA; C) ASA
Step-by-step explanation:
AAS is the Angle-Angle-Side congruence statement. It says that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of a second triangle, then the triangles are congruent. In these triangles, ∠E≅∠K, ∠F≅∠L, and DE≅JK. These are two angles and a non-included side; this is AAS.
LA is the leg-acute theorem. It states that if a leg and acute angle of one triangle is congruent to the corresponding leg and acute angle of another triangle, then the triangles are congruent.
The leg we have congruent from each triangle is DE and JK. We also have ∠E≅∠K and ∠F≅∠L, both pairs of which are acute. This is the LA theorem.
ASA is the Angle-Side-Angle congruence statement. It says that if two angles and an included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent.
We have that ∠D≅∠J, DE≅JK and ∠E≅∠K. This gives us two angles and an included side, or ASA.
Answer:
129 = x
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
47+82 = x
129 = x
The top box on the page explains the idea completely.
You need to read the top box several times, and understand it.
A ratio is a comparison of two quantities by division.
1). Days in May: 31
Days in a year: 365
Their ratio: 31/365 .
2). Sides of a triangle: 3
Sides of a square: 4
Their ratio: 3/4 .
The middle box explains how two ratios can be equal,
and it gives you a very detailed example. You should
read the middle box and understand it.
Ratios are fractions. They can be equal in just the same
way that any two fractions can be equal.
And you can simplify ratios in exactly the same way that
you simplify fractions ... divide top and bottom both by
the same number.
3). 8/12 Cook up three equal ratios.
1. divide top and bottom by 2 . . . . . 4/6
2. divide top and bottom by 4 . . . . . 2/3
3. multiply top and bottom by 9 . . . . 72/108
These are just some that I chose.
There are millions of others.
4). 20/25 Cook up three equal ratios.
1. divide top and bottom by 5 . . . . . 4/5
2. multiply top and bottom by 4 . . . . 80/100
3. multiply top and bottom by 3 . . . . 60/75
These are just some that I chose.
There are millions of others.
5). 5/6 Cook up three equal ratios.
1. multiply top and bottom by 2 . . . . 10/12
2. multiply top and bottom by 3 . . . .
3. multiply top and bottom by 9 . . . . 45/54
These are just some that I chose.
There are millions of others.
6). 10/14 Cook up three equal ratios.
1. divide top and bottom by 2 . . . . 5/7
2. multiply top and bottom by 2 . . . .
3. multiply top and bottom by (you choose) . . . .
Answer:
X=-3.0000067399190957
Y=-3.999994945051806
Step-by-step explanation:
